Van Gaal was reluctant to accept that his side had struggled in the first 30 minutes of the game, when they conceded the first of Graziano Pelle's two goals.

Asked whether his team needed to score more goals to make up for defensive inefficiencies, he said: "I don't agree with you. Have you seen the goal average against?

"Also, last season, all the media was writing the defence is very bad, but at the end, we were third (least conceded) in the Premier League (United were fourth for goals against).

"You say something and don't think about what you are saying."

When it was put to Van Gaal that Koeman had pointed out the weaknesses of his team's defence, the United manager first accused the media of having misquoted his opposite number.

When it was pointed out that Koeman had indeed said just that, Van Gaal described the observation in question as "remarkable".

Van Gaal said that his team's struggles were down to tiredness from their Champions League exertions in midweek against PSV Eindhoven.

He took Matteo Darmian off at half-time after a poor first half and later replaced Marcos Rojo with Paddy McNair, who played at centre-back.

Van Gaal said he replaced Darmian with Antonio Valencia to deal with the threat of Dusan Tadic.

"He (Darmian) gives too much space on Tadic in my opinion and Tadic was the most dangerous man.

"That is why I have changed him and Valencia did very well - I didn't see Tadic any more in the second half."

Van Gaal praised Anthony Martial's talent, adding that he expected the teenager's form to go through some peaks and troughs.

"You cannot expect consistency from a player of 19 years old. Emotionally, they shall have a lot of dips, so that I expect also from him, but that is not a big problem for me.

"I'm very happy that he is in three matches and his talent is at a high level. He adapts to the system of how we want to play, that is also important - not every player can adapt in that system.

"He scores goals. That is the most important thing."

As he left his press briefing, a thought occurred to van Gaal and he paused to ask a question of his own about the Dutch manager in the opposing dugout, for whom he famously has so little regard.

"Did Koeman say that they deserved to win?" he asked, in the manner of a man seeking an answer that he knew would displease him.

In fact, Koeman had said nothing of the sort - more that Southampton had thrown the game away rather than allow themselves to be outplayed by Manchester United over the course of a match in which the away team wrestled back control and then lost it again.

Koeman said he had told his players not to hit back-passes to the goalkeeper of the kind that Maya Yoshida did for the second United goal.

"I hate players who always hit the ball back to the goalkeeper - there were several moments in the game where you put the pressure on them. We saw the weaknesses of Manchester United today, defensively.

"I will tell them the same story (about back-passes), it is always a risk. We have to learn from that because we made that mistake last year."